Solve the system of equations.

Question

-6x+2y=-32
4x+3y=-9

Answer 1

To solve this system of equations, we can use the method of substitution.

We have the equations:
-6x + 2y = -32
4x + 3y = -9

Let's start by solving the first equation for x:
-6x + 2y = -32
=> -6x = -2y - 32
=> x = (2y + 32)/6
=> x = (1/3)y + 16/3

Now, substitute this value of x into the second equation:
4((1/3)y + 16/3) + 3y = -9
=> (4/3)y + 64/3 + 3y = -9
=> 4y + 64 + 9y = -27
=> 13y + 64 = -27
=> 13y = -91
=> y = -91/13
=> y = -7

Now, substitute the value of y back into the equation we solved for x:
x = (1/3)y + 16/3
=> x = (1/3)(-7) + 16/3
=> x = -7/3 + 16/3
=> x = 9/3
=> x = 3

Therefore, the solution to the system of equations is x = 3 and y = -7.